Place the bacon on a baking sheet and bake to the desired crispness, 12 to 15 minutes.
Meanwhile, quarter the potatoes and place them and the garlic in a medium pot with cold water to cover; add salt. Bring to a boil over high heat, then lower the heat and simmer until potatoes are fully cooked and soft, about 15 minutes. Drain well.
While potatoes are cooking, start on the omelet filling: Cut the onion into small dice; you'll need 1/2 cup. Remove and discard the stems from the mushrooms, then thinly slice the caps. Seed the tomatoes and cut into small dice.
In a skillet over medium heat, sweat half of the onions, seasoned with salt, in some olive oil until translucent and soft, about 5 minutes. Add the mushrooms, season with salt, and continue cooking until slightly soft, another 5 minutes. Add the tomatoes; cook for 3 to 4 more minutes. Add salt to taste.
Whisk the eggs together with 2 tablespoons water and 1/2 teaspoon salt until fluffy. Set aside.
Heat a cast-iron skillet over medium-high heat; add olive oil to coat the pan. Add the remaining 1/4 cup diced onions and cook for 2 minutes. Add the potatoes; cook until golden brown and crispy, about 6 minutes.
Place a nonstick skillet over medium heat; add olive oil to coat. Add the egg mixture and cook until set, frequently moving the edges away from the pan with a rubber spatula. Sprinkle with a layer of shredded fontina, add the filling to the middle, and fold the omelet. Cook until the cheese has melted, another minute or two.
Arrange all--bacon, home fries and omelet--on a serving platter, sprinkle with fresh chives, and serve with pumpernickel toast on the side.